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Equations with Variables/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby. Tim, a boy, and his robot friend Moby are standing in a backyard, staring at a tree house. Moby is surrounded by scattered pieces of wood, a saw, and a hammer. The tree house is perched high above them, but it has no ladder. TIM: Good job on the tree house, Moby! Um. How are we supposed to get up there? Moby beeps and shrugs. Tim pulls a letter from his pocket. Text reads as Tim narrates: TIM: Dear Tim and Moby; when those letters are all over math problems, I have no idea what to do. From, Ned. You're talking about algebra. That’s the branch of math where you solve equations with variables. A label appears, reading, algebra. Moby beeps and looks confused. TIM: Well, an equation is a comparison of two sets of numbers with an equals sign. A label appears, reading, equation. TIM: Like, 2 plus 3 equals 5 is an equation. The quantities on each side of the equals sign have to be…well, equal! An equation appears, reading, 2 plus 3 equals 5. The equals sign is highlighted. TIM: A variable is a placeholder for a number we don’t know yet—so instead, we use a letter. A label appears, reading, variable. Three identical equations appear. Each one reads 2 plus 3 equals 5. Suddenly, one number in each equation changes to a question mark. The first equation now reads, question mark plus 3 equals 5. The second reads, 2 plus 3 equals question mark. The third reads, 2 plus question mark equals 5. TIM: Whether it’s an x, a y, an a, or some other letter, a variable is just an unknown number. On-screen, variables replace the question marks in the three equations. Now they read: a, plus 3 equals 5; 2 plus 3 equals c; and 2 plus x equals 5. TIM: The numbers in an equation are called constants, because their value is set. A label appears, reading, constant. On-screen, the numbers in each equation are highlighted. TIM: You can think of equations with variables like a fill-in-the-blank question. On-screen, all three variables turn into blanks. Now the equations read: Blank plus 3 equals 5; 2 plus 3 equals blank; and 2 plus blank equals 5. TIM: The purpose of an equation with a variable is to fill in that blank—in other words, find out which number makes each side of the equation equal. Moby beeps and shrugs his shoulders. TIM: What do you mean, so what? We can use variables to build a ladder for this tree house! How high is the tree house? Moby extends his metal legs and, with a whirring sound, stretches up to the level of the tree house. After a moment, he descends and beeps. TIM: So, our ladder needs to be 5 meters high. Moby throws up his arms triumphantly. TIM: Well, we're not done yet. Moby looks disappointed. TIM: It just so happens that we have two 5-meter-long pieces of wood. On-screen, 2 planks of wood appear. Each is labeled, 5 meters. TIM: But a ladder needs rungs; those things you step on. On-screen, the 2 planks are joined by rungs, making a ladder. TIM: I think we’re gonna need to solve some equations to make this ladder. Moby beeps. On-screen, the ladder loses its rungs, which become a heap of wooden slats. TIM: We've got 21 of these wooden slats to use as rungs. We'll make them all the same distance apart so the ladder is safe. On-screen, the slats appear between the planks at evenly spaced intervals, forming a ladder again. TIM: We need to figure out how far apart the rungs should be. On-screen, the space between one pair of rungs is highlighted. TIM: Here’s where an equation comes in handy. The distance we’re trying to find can be expressed as a variable, say, d. On-screen, the letter d, appears. TIM: It’s the value that we don’t know. With 21 slats, it takes 20 of our unknown distances to make 5 meters. On-screen, the space between each pair of rungs is marked with a d. There are 20 spaces in all. The length of the entire ladder is labeled, 5 meters. TIM: That can be expressed as an equation: 20 times d equals 5. An equation appears, reading, 20 times d, equals 5. TIM: To solve an equation, you need to isolate the variable on one side of the equation. That way, you can compare what you're not sure of with real numbers that you are sure of. We need to get rid of that times 20, so we can divide that side by 20 to cancel it out. On-screen, the equation changes to read, 20 times d, over 20, equals 5. Moby beeps triumphantly again. TIM: Hold on, we're not done yet. Whenever you do something to one side of the equation, you have to do the same thing to the other side to keep the two sides equal. On-screen, the equation changes to read, 20 times d, over 20, equals 5 over 20. Moby looks confused and beeps. TIM: Okay, easy part first: 20 divided by 20 equals 1 and 1 times d is the same as d. On-screen, the left half of the equation changes to read, 1 times d, then to just d. The full equation now reads, d, equals 5 over 20. TIM: And 5 divided by 20 equals… 0.25. On-screen, the right side of the equation changes to read, 0.25. The full equation now reads, d, equals 0.25. TIM: So d, our unknown distance, equals 0.25 meters. The rungs of our ladder need to be 0.25 meters apart. On-screen, the ladder appears again. In the space between the rungs, the letter d, changes to 0.25 meters. Moby beeps and pulls a meter stick out from his tool belt. TIM: How many centimeters are in 0.25 meters? An equation appears, reading, 0.25 meters equals question mark centimeters. TIM: Mmm, that’s a different equation. We know that 1 meter equals 100 centimeters. On-screen, Moby's meter stick appears. A label appears above it, reading, 1 meter. Another label appears below it, reading, 100 centimeters. TIM: And we’ll call our unknown number of centimeters x. To find x, we need to multiply 0.25 by 100 centimeters. An equation appears, reading, x, equals 0.25 times 100. TIM: So, 100 times 0.25 equals 25. On-screen, the equation changes to, x, equals 25 centimeters. TIM: X, equals 25 centimeters. Looks right to me. The rungs of our ladder should be 0.25 meters; or 25 centimeters apart! On-screen, the ladder replaces the meter stick. A bracket measures the distance between one pair of rungs. Text above the bracket reads, 25 centimeters. Text below reads, 0.25 meters. TIM: So let's build that ladder so we can get up to the tree house! On-screen, Tim and Moby stand beneath the tree house. Tim looks at Moby’s building materials. TIM: Uhm. Where are the nails? Moby beeps, and closes his eyes smugly. TIM: What do you mean you don't use nails? Moby beeps again. There is a slow creaking sound from above. Tim looks up. The tree house sways and suddenly, with a loud crack of breaking wood, begins to collapse. Tim runs. TIM: Aggh! On-screen, the view goes dark. The tree house can be heard crashing to the ground. 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